Open-loop beamforming MIMO communications in frequency division duplex systems
Techniques are provided for wireless communication between a first wireless communication device and a second wireless communication device. At a plurality of antennas of the first wireless communication device, one or more signals transmitted by a second wireless communication device in a first frequency band are received. Beamforming weights are computed from information derived from the signals received at the plurality of antennas using one or more of a plurality of methods without feedback information from the second wireless communication device about a wireless link from the first wireless communication device to the second wireless communication device. The beamforming weights are applied to at least one transmit signal to beamform the at least one transmit signal for transmission to the second wireless communication device in a second frequency band.
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This application is a continuation-in-part of U.S. application Ser. No. 12/164,335, filed Jun. 30, 2008, and entitled “Orthogonal/Partial Orthogonal Beamforming Weight Generation For MIMO Wireless Communication,” the entirety of which is incorporated herein by reference.
TECHNICAL FIELDThe present disclosure relates to wireless communication devices and systems and more particularly to beamforming in frequency division duplex wireless communication systems.
BACKGROUNDIn wireless communication systems, antenna arrays are used at devices on one or both ends of a communication link to suppress multipath fading and interference and to increase system capacity by supporting multiple co-channel users and/or higher data rate transmissions. In a frequency division duplex (FDD) system, configuring a base station equipped with an antenna array to achieve improved downlink multiple-input multiple-output (MIMO) transmission performance is more difficult than improving the performance on an associated uplink due to a lack of information of estimated downlink channel coefficients. In general, a downlink channel covariance can be used to determine the downlink beamforming weights. However, in many situations an uplink channel covariance cannot be used to compute predicted or candidate downlink beamforming weights. In a FDD wireless communication system, the base station may not have the instantaneous downlink channel covariance matrix unless there is feedback information provided by a mobile station to the base station. Feedback of downlink channel information increases the overhead placed on the communication channel and therefore reduces the uplink channel capacity. Thus, it is preferable to avoid the reliance on feedback information when possible.
Overview
Techniques are provided for wireless communication between a first wireless communication device and a second wireless communication device. At a plurality of antennas of the first wireless communication device, one or more signals transmitted by a second wireless communication device in a first frequency band are received. Beamforming weights are computed from information derived from the signals received at the plurality of antennas using one or more of a plurality of methods without feedback information from the second wireless communication device about a wireless link from the first wireless communication device to the second wireless communication device. The beamforming weights are applied to at least one transmit signal to beamform the at least one transmit signal for transmission to the second wireless communication device in a second frequency band.
Referring first to
The BS 10 comprises a plurality of antennas 18(1)-18(M) and the MS's 20(1)-20(K) may also comprise a plurality of antennas 22(1)-22(P). The BS 10 may wirelessly communicate with individual ones of the MS's 20(1)-20(K) using a wideband wireless communication protocol in which the bandwidth is much larger than the coherent frequency bandwidth. An example of such a wireless communication protocol is the IEEE 802.16 communication standard, also known commercially as WiMAX™.
Techniques are provided herein to compute values for beamforming weights that a first communication device, e.g., the BS 10, uses for multiple-input multiple-output (MIMO) wireless communication of multiple signal streams to a second communication device, e.g., MS 20(1). The BS 10 generates the beamforming weights based on the uplink channel information from the MS 20(1).
The following description makes reference to generating beamforming weights for a MIMO transmission process in frequency division duplex (FDD) or time division duplex (TDD) orthogonal frequency division multiple access (OFDMA) systems as an example only. These techniques may easily be extended to processes of beamforming weights generation in any FDD/TDD MIMO wireless communication system. The approach described herein uses relatively low complexity (and thus requires reduced processing resources) that can significantly improve the process of downlink beamforming in macrocell/microcell FDD/TDD MIMO systems in multipath environments.
Generally, the BS 10 computes a sequence of orthogonal or partially orthogonal (orthogonal/partially orthogonal) beamforming weights {ŵi}i=1N
Turning to
The transmitter 12 may comprise individual transmitter circuits that supply respective upconverted signals to corresponding ones of a plurality of antennas (antennas 18(1)-18(M)) for transmission. To this end, the transmitter 12 comprises a MIMO beamforming signal stream generation module 90 that applies the sequence of beamforming weights {ŵi}i=1N
The controller 16 comprises a memory 17 or other data storage block that stores data used for the techniques described herein. The memory 17 may be separate or part of the controller 16. Instructions for performing an orthogonal/partial orthogonal beamforming weight generation process 100 may be stored in the memory 17 for execution by the controller 16. The process 100 generates the sequence of beamforming weights {ŵi}i=1N
The functions of the controller 16 may be implemented by logic encoded in one or more tangible media (e.g., embedded logic such as an application specific integrated circuit, digital signal processor instructions, software that is executed by a processor, etc.), wherein the memory 17 stores data used for the computations described herein (and/or to store software or processor instructions that are executed to carry out the computations described herein). Thus, the process 100 may be implemented with fixed logic or programmable logic (e.g., software/computer instructions executed by a processor). Moreover, the functions of the MIMO beamforming signal stream generation module 90 and the orthogonal/partial orthogonal beamforming weight generation process 100 may be performed by the same logic component, e.g., the controller 16.
A brief description of an OFDMA signaling scheme, such as the one used in a WiMAX system, is described by way of background. The OFDMA symbol structure comprises three types of subcarriers: data subcarriers for data transmission, pilot subcarriers for estimation and synchronization purposes, and null subcarriers for no transmission but used as guard bands and for DC carriers. Active (data and pilot) subcarriers are grouped into subsets of subcarriers called subchannels for use in both the uplink and downlink. For example, in a WiMAX system, the minimum frequency-time resource unit of sub-channelization is one slot, which is equal to 48 data tones (subcarriers).
Furthermore, in a WiMAX system there are two types of subcarrier permutations for sub-channelization; diversity and contiguous. The diversity permutation allocates subcarriers pseudo-randomly to form a sub-channel, and in so doing provides for frequency diversity and inter-cell interference averaging. The diversity permutations comprise a fully used subcarrier (FUSC) mode for the downlink and a partially used subcarrier (PUSC) mode for the downlink and the uplink. In the downlink PUSC mode, for each pair of OFDM symbols, the available or usable subcarriers are grouped into “clusters” containing 14 contiguous subcarriers per symbol period, with pilot and data allocations in each cluster in the even and odd symbols.
A re-arranging scheme is used to form groups of clusters such that each group is made up of clusters that are distributed throughout a wide frequency band space spanned by a plurality of subcarriers. The term “frequency band space” refers to the available frequency subcarriers that span a relatively wide frequency band in which the OFMDA techniques are used. When the FFT size L=128, a sub-channel in a group contains two (2) clusters and is made up of 48 data subcarriers and eight (8) pilot subcarriers. When the FFT size L=512, a downlink PUSC subchannel in a major group contains some data subcarriers in ten (10) clusters and is made up of 48 data subcarriers and can use forty (40) pilot subcarriers.
The data subcarriers in each group are further permutated to generate subchannels within the group. The data subcarriers in the cluster are distributed to multiple subchannels.
The techniques described herein are applicable to the downlink beamforming generation process in any MIMO wireless communication system that requires estimating accurate downlink channel coefficients, such as in FDD/TDD CDMA (code division multiple access) systems, or FDD/TDD OFDMA systems. The following description is made for a process to generate multiple downlink beamforming weights in a MIMO FDD/TDD OFDMA system, as one example. The adaptive downlink beamforming weights are generated with a combination of beamforming weight prediction and an orthogonal computation process. The multiple beamforming weights are orthogonal or partially orthogonal and may be used for space-time coding transmissions or MIMO transmissions in WiMAX system, for example.
The BS computes a channel covariance for every MS if every MS experiences different channel conditions. To do so, the BS computes estimated uplink channel coefficients in the frequency domain for a MS based on signals received from that MS, as HUL=[HUL,1 HUL,2 . . . HUL,M]T, where T stands for Transpose operation, ‘UL’ stands for uplink and M is the number of antennas at the BS. RUL is the uplink channel covariance
and average uplink channel covariance, where Ne is the number of received signals ([1,∞)) with the same direction of arrivals (DOAs) during a coherence time interval (i.e., the time interval during which phase and magnitude of a propagating wave are, on average, predictable or constant) and H stands for Hermitian operation.
Turning now to
At 120, the first candidate beamforming weight vector w1 from the sequence of candidate beamforming weight vectors {wn}n=1N
The functions associated with 130-170 involve computing a sequence of orthogonal/partially orthogonal beamforming weight vectors {ŵi}i=1N
At 130, for the ith orthogonal/partially orthogonal beamforming weight vector ŵi (for i≧2), projections are computed between the ith candidate beamforming weight vector wi and all previous (1 to i−1) orthogonal/partially orthogonal beamforming weight vectors. This projection computation may be represented by the equation:
where α and β are practical weighted scalars. For example, α=1.2 and β=1, or α=1 and β=0.8, or α=1 and β=1. These projections constitute the spatial overlap to a candidate beamforming vector.
At 140, the projections computed at 130 are subtracted from the ith candidate beamforming vector:
Thus, the result of this subtraction is a vector that is orthogonal to all of the prior vectors in the sequence {ŵi}i=1N
At 150, the ith orthogonal/partially orthogonal beamforming weight vector is normalized to boost the power associated with its orthogonal portion:
ŵi=ŵi/norm(ŵ1).
The functions of 130-170 are repeated for each beamforming weight vector in the sequence {ŵi}i=1N
There are several methods for estimating/computing the candidate beamforming weights at 110. Examples of several methods that can be used separately or in combination are now described. In one example, a set of candidate beamforming weight vectors is computed using each of a plurality of methods or techniques to produce a plurality of sets of candidate beamforming weight vectors. Correlation rate and predicted average beamforming performance among candidate beamforming weight vectors within each set is determined and one of the plurality of sets of candidate beamforming weight vectors is selected based on the degree of correlation and predicted average beamforming performance among its candidate beamforming weight vectors. The sets of candidate beamforming weight vectors may be prioritized by the correlation rate and predicted average beamforming performance, whereby the set of candidate beamforming weight vectors with the lowest correlation and best predicted average beamforming performance is given the highest priority and the set of candidate beamforming weight vectors with the highest correlation is given the lowest priority.
Normalized Average Estimate of Uplink Channel Coefficients—Method 1
One technique to compute the candidate beamforming weights is to set the beamforming weight was the normalized average of the estimated uplink channel coefficient, w=
DOA Method—Method 2
Reference is now made to
Use of Channel Covariance Matrix—Method 3
Reference is now made to
Another Use of Channel Covariance Matrix—Method 4
Reference is made to
Ne is the number of received signals [1, ∞) with the main DOAs in the coherence time and H stands for Hermitian operation. At 224, the M eigenvectors {U1, U2, . . . , UM} of the average uplink channel covariance matrix are computed. Then, at 226, values for the candidate beamforming weight vectors are computed based on a weighted linear combination of the eigenvectors, such as, w=(c1U1+c2U2+ . . . +cMUM)/norm(c1U1+c2U2+ . . . +cMUM), where {cj}j=1M are complex weighting values (some of which may be set to zero).
Channel Covariance Matrix Method for FDD Systems—Method 5
Turning now to
Spatial Subspace Decomposition Method—Method 6
Referring to
where D is the distance between two adjacent antennas, and for a uniform circular array (UCA),
where r is the radius of the circular array.
Channel Tap-Based Method—Method 7
Using any one or more of the methods described above, ξ beamforming weights can be computed and then those weights used to regenerate a covariance matrix, also referred to as a “new” covariance matrix. For example, the two column vectors of beamforming weights as {w1,w2} are used to generate a covariance matrix {circumflex over (R)} as {circumflex over (R)}=w1w1H+w2w2H. The singular value decomposition may then be computed on the regenerated covariance matrix to obtain the eigenvectors. New or updated values for the candidate beamforming weights may then be set as the principle (or any) eigenvector of the generated covariance matrix, or the combination of eigenvectors. If M eigenvectors of the generated covariance matrix {circumflex over (R)} are {Û1, Û2 . . . , ÛM} corresponding to the eigenvalues {{tilde over (Λ)}1, {tilde over (Λ)}2, . . . , {tilde over (Λ)}M}, then the beamforming weights may be set as Û1 or/and Û2.
Many of the beamforming weight computation methods described above in connection with
In an FDD communication system such as that depicted in
Generally, the BS 10′ computes beamforming weights {ŵi}i=1N
Turning to
Like the BS 10 shown in
The BS 10′ computes a channel covariance for every MS if every MS experiences different channel conditions. To do so, the BS 10′ computes estimated uplink channel coefficients in the frequency domain for an MS based on signals received from that MS, as HUL=[HUL,1 HUL,2 . . . . HUL,M]T, where T stands for Transpose operation, ‘UL’ stands for uplink and M is the number of antennas at the BS 10′. As explained above in connection with
where Ne is the number of received signals ([1, ∞)) with the same direction of arrivals (DOAs) during a coherence time interval (i.e., the time interval during which phase and magnitude of a propagating wave are, on average, predictable or constant) and H stands for Hermitian operation.
Turning to
from the estimated uplink channel matrix HUL. At 316, the BS selects a beamforming weight computation method according to the transmission scheme to be used for a downlink transmission to the MS. For example, the downlink transmission scheme may be beamforming one or more (MIMO) signal streams, spatial multiplexing (with beamforming), or space-time coding (with beamforming). At 318, a selected method, or a combination of methods, are invoked (performed) to compute the beamforming weights depending on the downlink transmission scheme to be employed by the BS 10′.
As between a first wireless communication device and a second wireless communication device, the process 300 depicted by
Any one of the beamforming weight vector computation methods described above in connection with
Another Regenerated Covariance Matrix Method—Method 8
Based on any of the beamforming weight computation methods described above, a sequence of beamforming weight vectors {wn}n=1N
After generating the Nw beamforming weight vectors based on the methods described above, Nw virtual antennas are created at the BS 10′. The Nw beamforming weight vectors are applied to Nw transmit signal streams to produce Nw beamformed streams that are transmitted on the downlink to a MS.
The particular transmission scheme employed when transmitting the Nw transmit signal streams may vary, and the method employed to compute the beamforming weights is selected according to the transmission scheme as indicated at 316 in
When the downlink transmission scheme is space-time coding with beamforming, Methods 2, 3 or 8 described above are useful. When the downlink transmission scheme is spatial multiplexing with beamforming, the Methods 3, 7 or 8 are useful.
The techniques for computing beamforming weight vectors described herein significantly improve the downlink beamforming performance with low computation complexity, particularly when accurate downlink channel coefficients are not directly available because there is no feedback information sent by a MS to the BS.
Although the apparatus, system, and method are illustrated and described herein as embodied in one or more specific examples, it is nevertheless not intended to be limited to the details shown, since various modifications and structural changes may be made therein without departing from the scope of the apparatus, system, and method and within the scope and range of equivalents of the claims. Accordingly, it is appropriate that the appended claims be construed broadly and in a manner consistent with the scope of the apparatus, system, and method, as set forth in the following claims.
Claims
1. A method comprising:
- at a plurality of antennas of a first wireless communication device, receiving one or more signals transmitted by a second wireless communication device in a first frequency band;
- computing a set of candidate beamforming weight vectors using each of the plurality of methods to produce a plurality of sets of candidate beamforming weight vectors without feedback information from the second wireless communication device about a wireless link from the first wireless communication device to the second wireless communication device;
- computing a correlation rate and predicted average beamforming performance among candidate beamforming weight vectors within each set; and
- selecting one of the plurality of sets of candidate beamforming weight vectors based on a degree of correlation and predicted average beamforming performance among its candidate beamforming weight vectors; and
- applying the selected one of the plurality of sets of candidate beamforming weight vectors to multiple signal streams to beamform the multiple signal streams for transmission to the second wireless communication device in a second frequency band.
2. The method of claim 1, wherein computing beamforming weight vectors comprises computing a plurality of beamforming weight vectors in each candidate set of beamforming weight vectors, and wherein applying comprises applying the selected one of the plurality of sets of candidate beamforming weight vectors to corresponding ones of the multiple signal streams for beamforming the multiple signal streams to the second device.
3. The method of claim 1, wherein computing the beamforming weight vectors comprises computing an estimated uplink channel covariance matrix from the signals received at the plurality of antennas, and computing a norm of the estimated uplink channel covariance matrix.
4. The method of claim 1, wherein computing the beamforming weight vectors comprises computing direction of arrival data associated with the signals received at the plurality of antennas, generating data for a column vector A(θ,λ) that represents a response vector associated with the signals received at the plurality of antennas for each of a plurality of direction of arrivals {θ1, θ2,..., θL}, where λ is the carrier wavelength of the one more receive signals, and setting the beamforming weight vectors based on elements of the response vector for at least one the plurality of direction of arrivals.
5. The method of claim 1, wherein computing the beamforming weight vectors comprises computing direction of arrival data associated with the signals received at the plurality of antennas, computing a covariance matrix associated with the direction of arrival data, computing a singular value decomposition from the covariance matrix to obtain a plurality of eigenvectors of the new covariance matrix, and setting the beamforming weight vectors to values based on multiple eigenvectors of the covariance matrix.
6. The method of claim 1, wherein computing the beamforming weight vectors comprises computing an average uplink channel covariance from the signals received at the plurality of antennas, computing eigenvectors of the average uplink channel covariance matrix, and setting the beamforming weight vectors to values based on multiple eigenvectors of the average uplink channel covariance matrix, or a linear combination of the eigenvectors of the average uplink channel covariance matrix.
7. The method of claim 1, wherein computing the beamforming weight vectors comprises computing an average uplink channel covariance from the signals received at the plurality of antennas, computing an estimated downlink channel covariance from the average uplink channel covariance and a transformation matrix that is based on the number of antennas of the first device, the spacing of the antennas at the first wireless communication device and a number of spatial sectors, computing eigenvectors of the estimated downlink channel covariance matrix, and setting the beamforming weight vectors to values based on multiple eigenvectors of the average downlink channel covariance.
8. The method of claim 1, wherein computing the beamforming weight vectors comprises computing an estimate of maximum direction of arrivals associated with the signals received at the plurality of antennas and complex-valued projections of the maximum direction of arrivals, applying a group of random variation factors {fk}k=1K to the complex-valued projection and maximum direction of arrivals, and computing the beamforming weight vectors from the maximum direction of arrivals and the complex-valued projections.
9. The method of claim 1, wherein computing the beamforming weight vectors comprises computing an average uplink channel covariance from the signals received at the plurality of antennas, computing J maximum estimated channel taps in a time domain h=[h1 h2... hJ] with the time delays τ=[τ1 τ2... τJ] from the average uplink channel covariance, applying a group of complex random factors {gk}k=1J to the estimated channel taps and time delays, and computing the beamforming weight vectors using the estimated channel taps and time delays.
10. The method of claim 1, and further comprising computing an estimated uplink channel covariance matrix from the signals received at the plurality of antennas, computing the beamforming weight vectors from the estimated uplink channel covariance matrix, computing a new covariance matrix from the beamforming weights, computing a singular value decomposition of the new covariance matrix to produce a plurality of eigenvectors and setting values for the beamforming weight vectors based on multiple eigenvectors.
11. The method of claim 1, and further comprising prioritizing the sets of candidate beamforming weight vectors by correlation rate and predicted average beamforming performance such that the set of candidate beamforming weight vectors with a lowest correlation and best predicted average beamforming performance is given a highest priority and the set of candidate beamforming weight vectors with a highest correlation is given a lowest priority.
12. An apparatus comprising:
- a plurality of antennas;
- a receiver that is configured to process signals received at the plurality of antennas, which signals were transmitted in a first frequency band by another communication apparatus;
- a controller coupled to the receiver, wherein the controller is configured to: compute a set of candidate beamforming weight vectors using each of the plurality of methods to produce a plurality of sets of candidate beamforming weight vectors without feedback information from the other communication apparatus about a wireless link from the plurality of antennas to the other communication apparatus; compute a correlation rate and predicted average beamforming performance among candidate beamforming weight vectors within each set; and select one of the plurality of sets of candidate beamforming weight vectors based on a degree of correlation and predicted average beamforming performance among its candidate beamforming weight vectors; and
- a transmitter coupled to the controller, wherein the transmitter is configured to apply the selected one of the plurality of sets of candidate beamforming weight vectors to multiple signal streams to beamform multiple signal streams for transmission in a second frequency band via the plurality of antennas to the other communication apparatus.
13. The apparatus of claim 12, wherein the controller is configured to compute a plurality of beamforming weight vectors in each candidate set of beamforming weight vectors, and wherein the transmitter is configured to apply the selected one of the plurality of sets of candidate beamforming weight vectors to corresponding ones of the multiple signal streams for beamforming the multiple signal streams to the other communication apparatus.
14. The apparatus of claim 12, wherein the controller is configured to compute the beamforming weight vectors by computing direction of arrival data associated with signals received at the plurality of antennas, generating data for a column vector A(θ,λ) that represents a response vector associated with the signals received at the plurality of antennas for each of a plurality of direction of arrivals {θ1, θ2,..., θL,}, where λ is the carrier wavelength of the one more receive signals, and setting the beamforming weight vectors based on elements of the response vector for at least one the plurality of direction of arrivals.
15. The apparatus of claim 12, wherein the controller is configured to compute the beamforming weight vectors by computing an estimate of maximum direction of arrivals associated with the signals received at the plurality of antennas and complex-valued projections of the maximum direction of arrivals, applying a group of random variation factors {fk}k=1K to the complex-valued projection and direction of arrivals, and computing the beamforming weight vectors from the maximum direction of arrivals and the complex-valued projections.
16. The apparatus of claim 12, wherein the controller is configured to compute the beamforming weight vectors by computing an average uplink channel covariance matrix from the signals received at the plurality of antennas, computing eigenvectors of the average uplink channel covariance matrix, and setting the beamforming weight vectors to values based on multiple eigenvectors of the average uplink channel covariance matrix, or a linear combination of the eigenvectors of the average uplink channel covariance matrix.
17. The apparatus of claim 12, wherein the controller is further configured to compute an estimated uplink channel covariance matrix from the signals received at the plurality of antennas, compute the beamforming weight vectors from the estimated uplink channel covariance matrix, compute a new covariance matrix from the beamforming weight vectors, compute a singular value decomposition of the new covariance matrix to produce a plurality of eigenvectors and set values for the beamforming weight vectors based on multiple eigenvectors.
18. The apparatus of claim 12, wherein the controller is further configured to prioritize the sets of candidate beamforming weight vectors by correlation rate and predicted average beamforming performance such that the set of candidate beamforming weight vectors with a lowest correlation and best predicted average beamforming performance is given a highest priority and the set of candidate beamforming weight vectors with a highest correlation is given a lowest priority.
19. One or more tangible processor readable storage media storing instructions for execution by a processor and when executed operable to:
- compute a set of candidate beamforming weight vectors using each of the plurality of methods to produce a plurality of sets of candidate beamforming weight vectors without feedback information from the second device about a wireless link from the first device to the second device; compute a correlation rate and predicted average beamforming performance among candidate beamforming weight vectors within each set; and
- select one of the plurality of sets of candidate beamforming weight vectors based on a degree of correlation and predicted average beamforming performance among its candidate beamforming weight vectors; and
- apply the selected one of the plurality of sets of candidate beamforming weight vectors to multiple signal streams to beamform the multiple signal streams for transmission to the second device in a second frequency band.
20. The processor readable storage media of claim 19, wherein the instructions that are operable to compute the beamforming weight vectors comprise instructions operable to compute a plurality of beamforming weight vectors in each candidate set of beamforming weight vectors, and wherein the instructions that are operable to apply comprise instructions operable to apply the selected one of the plurality of sets of candidate beamforming weight vectors to corresponding ones of the multiple signal streams for beamforming the multiple signal streams to the other second device.
21. The processor readable storage media of claim 19, wherein the instructions operable to compute the beamforming weight vectors comprise instructions operable to compute an average uplink channel covariance matrix from the signals received at the plurality of antennas of the first device, compute eigenvectors of the average uplink channel covariance matrix, and set the beamforming weight vectors to values based on multiple eigenvectors of the average uplink channel covariance matrix, or a linear combination of the eigenvectors of the average uplink channel covariance matrix.
22. The processor readable storage media of claim 19, and further comprising instructions operable to compute an estimated uplink channel covariance matrix from the signals received at the plurality of antennas, compute the beamforming weight vectors from the estimated uplink channel covariance matrix, compute a new covariance matrix from the estimated multiple beamforming weight vectors, compute a singular value decomposition of the new covariance matrix to produce a plurality of eigenvectors and set values for the beamforming weight vectors based on multiple eigenvectors.
23. The processor readable storage media of claim 19, and further comprising instructions operable to prioritize the sets of candidate beamforming weight vectors by correlation rate and predicted average beamforming performance such that the set of candidate beamforming weight vectors with a lowest correlation and best predicted average beamforming performance is given a highest priority and the set of candidate beamforming weight vectors with a highest correlation is given a lowest priority.
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Type: Grant
Filed: Mar 13, 2009
Date of Patent: Mar 13, 2012
Patent Publication Number: 20090323847
Assignee: Cisco Technology, Inc. (San Jose, CA)
Inventors: Yanxin Na (Plano, TX), Hang Jin (Plano, TX)
Primary Examiner: Thomas Tarcza
Assistant Examiner: Fred H Mull
Attorney: Edell, Shapiro & Finnan, LLC
Application Number: 12/403,533